You have 8 cubes that look the same,but one is slightly heavier than the others. I can only have two weighings to determine the heavy cube.
What are the two ways that I can do this?
2007-02-11 18:23:40 · 5 answers · asked by Julie G 1 in Science & Mathematics ➔ Mathematics
One way:
Weigh 3 cubes against another 3.
If they are equal, then
weigh the remaining 2 against each other.
the heavier one is the odd one.
if they are not equal, then take the heavier group of 3
select 2 weight them against each other.
if they are equal, then
the one left out is the heaviest
if they are not equal, then
the heavier one is the odd one.
2007-02-11 18:31:55 · answer #1 · answered by verbalise 4 · 3⤊ 0⤋
Lets label the 8 cubes from 1 to 8.
Weigh 1, 2, 3 against 4, 5, 6.
3 cases are possible
A> The weights are balanced
B> 1, 2, 3 is heavier
C> 4, 5, 6 is heavier
If Case A is true, then we just have to weigh 7 against 8 and the heavier cube can be determined amongst the two.
If Case B is true, then heavier cube is either 1, 2 or 3. The other cubes are all fine.
So we need to weigh 1, 4, 5 vs. 2, 6, 7.
If both are balanced then 3 is the heavier cube.
If 1, 4, 5 is heavier then 1 is the heavier cube.
If 2, 6, 7 is heavier then 2 is the heavier cube.
If Case C is true, then heavier cube is 4, 5 or 6. The other cubes are all fine.
So we need to weigh 4, 1, 2 vs. 5, 3, 7.
If both are balanced then 6 is the heavier cube.
If 4, 1, 2 is heavier then 4 is the heavier cube.
If 5, 3, 7 is heavier then 5 is the heavier cube.
2007-02-12 02:45:06 · answer #2 · answered by Nimish A 3 · 0⤊ 0⤋
You got many solutions in the time that I figuired it out and then the computer did not allow me to post the solution. Here it is:
Let us label them 1 to 8. Take 1,2,3 on one side of the balance and 4,5,6 on the other side.
Both sides are equal. We know that 7 or 8 must tbe the heavier one. So, wi\eigh 7 against 8. You will know which is heavier.
Suppose 1,2,3 is heavier than 4,5,6.
Take 1 and weigh against 2. If both are equal we know 3 is the heavy one. If one of them is heavier, we know that is the heavy one.
See that we have used only 2 weighing trials.
2007-02-12 02:45:18 · answer #3 · answered by Swamy 7 · 0⤊ 0⤋
I think this will work.
Put 4 on each side. The heavier side will be lower. Discard the 4 on the lighter side. Now divide the other 4 in half and put 2 on each side of the scale. One side will be lower. Remove one block from each side. One of two things will happen. If you happen to remove 2 that weigh the same then of the two left one side will be heavier and you will know which one. If you happen to remove one heavy one and one light one the scale will balance and you will know which one you removed is the heavier one because it came off the side of the scale that was lower.
2007-02-12 02:35:24 · answer #4 · answered by lizzie 3 · 0⤊ 0⤋
Use an equal arm balance .First divide them two parts like 4+4.
Which side is heavy than take they to measure second ly 2+2.See which side is heavy.So take them for the third trial.It means that you came theresult 1+1.
2007-02-12 02:30:55 · answer #5 · answered by Tuncay U 6 · 0⤊ 1⤋